ScalingStacks

Remark 2.22 . [03NH]

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Remark 2.22.

We need MM to be (symplectic) Calabi–Yau and L,L′L,L^{\prime} to be graded to define the degree μL,L′(p)∈ℤ\mu_{L,L^{\prime}}(p)\in{\mathbin{\mathbb{Z}}}, which determines the grading of C​F∗​((L,E),(L′,E′))CF^{*}\bigl((L,E),(L^{\prime},E^{\prime})\bigr) and H​F∗​((L,E,b),(L′,E′,b′))HF^{*}\bigl((L,E,b),(L^{\prime},E^{\prime},b^{\prime})\bigr). If we took MM symplectic and L,L′L,L^{\prime} oriented, then C​F∗​((L,E),(L′,E′)),H​F∗​((L,E,b),(L′,E′,b′))CF^{*}\bigl((L,E),(L^{\prime},E^{\prime})\bigr),HF^{*}\bigl((L,E,b),(L^{\prime},E^{\prime},b^{\prime})\bigr) would only be graded over ℤ2{\mathbin{\mathbb{Z}}}_{2} rather than ℤ{\mathbin{\mathbb{Z}}}.

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